In 1963 Glauber introduced the modern theory of quantum coherence, which extended the concept of first-order (onebody) correlations, describing phase coherence of classical waves, to include higher-order (n-body) quantum correlations characterizing the interference of multiple particles. Whereas the quantum coherence of photons is a mature cornerstone of quantum optics, the quantum coherence properties of massive particles remain largely unexplored. To investigate these properties, here we use a uniquely correlated source of atoms that allows us to observe n-body correlations up to the sixth order at the ideal theoretical limit (n!). Our measurements constitute a direct demonstration of the validity of one of the most widely used theorems in quantum many-body theory—Wick’s theorem—for a thermal ensemble of massive particles. Measurements involving n-body correlations may play an important role in the understanding of thermalization of isolated quantum systems and the thermodynamics of exotic many-body systems, such as Efimov trimers.